Transcript Calculator Paper Revision Higher

Calculator Paper
Revision Higher
Topic Index- These were not
on Paper 1
Mean Grouped
Frequency Table
Enlargement
negative/ fractional
scale factor
Cumulative
Frequency
Standard Form
Calculator
Reverse % (find the
original)
loci
Trig/ Pythagoras
Volume
Trig non right angled angle sum of
polygon
moving averages
Sybil weighed some pieces of
cheese.
The table gives information about her
results.
Weight (w) grams
Frequency
90 < w  94
1
94 < w  98
2
98 < w  102
6
102 < w  106
1
Work out an estimate of the mean weight.
.......................... grams
(4 marks)
back
At a supermarket, members of staff
recorded the lengths of time that 80
customers had to wait in the queues
at the check-outs.
The waiting times are grouped in
the frequency table opposite.
(a) Complete the
cumulative frequency
table opposite.
Waiting time (t seconds)
Frequency
0 < t  50
4
50 < t  100
7
100 < t  150
10
150 < t  200
16
200 < t  250
30
250 < t  300
13
Waiting time (t seconds)
0 < t  50
0 < t  100
0 < t  150
0 < t  200
0 < t  250
back
0 < t  300
Cumulative Frequency
In a sale, normal prices are reduced by 12%.
The sale price of a DVD player is £242.
Work out the normal price of the DVD player.
£ ............................
(3 marks)
—————————————————————————————————————————
A garage sells cars.
It offers a discount of 20% off the normal price for cash.
Dave pays £5200 cash for a car.
Calculate the normal price of the car.
£ ............................
(3 marks)
back
A statue stands on a column.
In the diagram AB represents the statue and BC represents the column.
Angle ACD = 90°.
Angle BDA = 2.8°.
AD = 91.2 m and BD = 88.3 m.
ABC is a vertical straight line.
(a) Calculate the height, AB, of the statue. Give your answer, in metres,
correct to 3 significant figures.
(3 marks)
(b) Calculate the height, BC, of the column. Give your answer, in metres,
correct to 3 significant figures.
(5 marks)
back
The diagram shows a trapezium.
AB is parallel to DC.
Angle A = 90°.
AB = 13 cm, AD = 6 cm and CD = 8 cm.
Calculate the size of angle B.
Give your answer correct to 1 decimal place.
............................ °
(4 marks)
back
The diagram shows triangle ABC.
AC = 7.2 cm.
BC = 8.35 cm.
Angle ACB = 74°.
(a) Calculate the area of triangle ABC.
Give your answer correct to 3 significant figures.
.............. , ..............
(3 marks)
(b) Calculate the length of AB.
Give your answer correct to 3 significant figures.
......................... cm
back
(3 marks)
back
Enlarge shape T with scale factor -1.5, centre (0, 2).
(3 marks)
(b) Enlarge shape A by scale factor 12 , centre (5, 16)
back
(a) Work out the value of
6
3  10
4
4  10
Give your answer in standard form.
(2 marks)
The distance from Earth to the star Proxima Centauri is 4.22 light years.
1 light year = 9.461 ´ 1012 km.
(b) Work out the distance in kilometres from Earth to the star Proxima Centau
Give your answer in standard form correct to 3 significant figures.
.................... km
(2 marks)
back
The diagram shows two points P and Q.
back
On the diagram shade the region which contains all the points that satisfy both
the following:the distance from P is less than 3 cm,
the distance from P is greater than the distance from Q. (3 marks)
The diagram represents a triangular garden ABC.
The scale of the diagram is 1 cm represents 1 m.
A tree is to be planted in the garden so that it is
nearer to AB than to AC,
within 5 m of point A.
On the diagram, shade the region where the tree may be planted.
back
back
The diagram shows a cylinder with a height of 10 cm and a radius of 4 cm.
(a) Calculate the volume of the cylinder.
Give your answer correct to 3 significant figures.
........................ cm3
(2 marks)
The length of a pencil is 13 cm.
The pencil cannot be broken.
(b) Show that this pencil cannot fit inside the cylinder. (3 marks)
back
The diagram shows a prism.
The cross-section of the prism is a trapezium.
The lengths of the parallel sides of the trapezium are 8 cm and 6 cm.
The distance between the parallel sides of the trapezium is 5 cm.
The length of the prism is 20 cm.
(a) Work out the volume of the prism.
.................. cm3
(3 marks)
back
ABCDEFGH is a regular octagon.
O is the centre of the octagon.
Calculate the size of angle AOF.
.................. °
(3 marks)
A shopkeeper recorded the number of books he sold every three months.
The table shows his records from January 2000 to June 2001.
Year
Months
2000
Jan  Mar
Apr  Jun
Jul  Sep
Number of books sold
83
122
56
Oct  Dec
Jan  Mar
210
82
Apr  Jun
104
2001
back
Calculate the complete set of three-point moving averages for this data.
...............................................................
(3 marks)